Question

A bank advertises the following deal: “Pay us $10,000 a year for 10 years, starting today and then we will pay you (or your beneficiaries) $10,000 at the beginning of year 11 and for every year after, forever.” Is this a good deal if the interest rate available on other deposits is 8%, compounded semi-annually?

Answer 1

Effective annual rate = (1+(r/m))^(m) -1 = 0.0816

where r is interest rate = 8% and m is no. of compounding periods =2

Effective annual rate = (1+(8%/2))^(2) -1 = 0.0816 = 8.16%

We need to compare future value of 10000 payments for 10 years at the end of year 10 with present value of perpetual payments of 10000 at the end of the year 10

Using financial calculator we get future value as follows:

PMT = 10000 N = 10 I/Y = 0.0816 CPT FV FV = $145970

PV = PMT/ r = 10000/ 0.0816 = $122549

Thus FV> PV at year 10 which implies you will be paying more than receiving .

Hence it is not a good deal.